Số số hạng của vế trái là:
\(\left(97-1\right):2+1=96:2+1=48+1=49\) (số)
Ta có: \(\left|x+\frac{1}{1\cdot3}\right|+\left|x+\frac{1}{3\cdot5}\right|+\cdots+\left|x+\frac{1}{97\cdot99}\right|=50x\)
=>50x>=0
=>x>=0
Phương trình sẽ trở thành:
\(x+\frac{1}{1\cdot3}+x+\frac{1}{3\cdot5}+\ldots+x+\frac{1}{97\cdot99}=50x\)
=>\(50x=49x+\left(\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\cdots+\frac{1}{97\cdot99}\right)\)
=>\(x=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\cdots+\frac{1}{97\cdot99}\)
=>\(x=\frac12\left(\frac{2}{1\cdot3}+\frac{2}{3\cdot5}+\cdots+\frac{2}{97\cdot99}\right)\)
=>\(x=\frac12\left(1-\frac13+\frac13-\frac15+\cdots+\frac{1}{97}-\frac{1}{99}\right)=\frac12\left(1-\frac{1}{99}\right)=\frac12\cdot\frac{98}{99}=\frac{49}{99}\)
